The stratified p-hub center and p-hub maximal covering problems

Hub networks are the foundation of many transportation and distribution systems, and real-world hub networks often transport freight or passengers of different service classes. This paper introduces the stratified multiple allocation p-hub center and p-hub maximal covering problems where the traffic corresponding to each origin–destination (O/D) pair is divided into different strata each having a specific service level requirement. The problems are formulated as mixed-integer linear programming (MILP) models and efficient Benders decomposition algorithms are developed for solving large instances. Extensive computational experiments are conducted to demonstrate the efficiency of the proposed mathematical models and the solution algorithms. MILP formulations are also proposed for the generalized versions of the problems that include fixed set-up costs for hubs and hub arcs. Results indicate that the optimal sets of hub locations and hub arcs when considering different strata can be quite dissimilar to those of the traditional p-hub center or p-hub maximal covering problem, but are similar to those of hierarchical hub location problems. Furthermore, models are provided and solved for multi-modal stratified hub location problems with fixed setup costs for hubs and hub arcs. Optimal results show a wide range of network topologies that can be generated, as compared to the classical versions.